Snow White(Show White and the seven Dwarfs), Sleeping Beauty(Sleeping Beauty), Princess Zelda(The Legend of Zelda, The Adventures of Link, A Link to the Past, Ocarina of Time, the Oracle Series, Four Swords), Princess Peach Toadstoal(some of the Mario games) and etc.

While the damsel in distress makes appearances in many folk stories dating back to Antiquity and features in a few fairy tales, this passive heroine does not seem to make regular appearances until the Victorian era; the Middle Ages were idealized as a time of pre-industrial innocence and the Victorians projected their ideals of men and women onto their Medieval ancestors; the Industrial Revolution was in full swing and women, displaced from farms and entering the middle class, lost some autonomy over their lives and became more ornamental, more dependent on their husbands.
Damsels in distress are often shown tied to railroad tracks, to sawmill conveyor belts, or offered as sacrifice to a dragon (or King Kong) until her knight in shining armor arrives to save her in the nick of time.

A damsel in distress would not have fared well in Medieval Europe. Generally, European women in the Middle Ages were not expected to be these timid shrinking violets; Christina of Markyate (who resisted a forced marriage and followed her dream of becoming a holy woman), Marjorie of Carrick, Christine de Pisan (a proto-feminist of sorts), Margery Kempe (another mystic), and Nicola de la Haye (led her castle against a siege in her 60s) are just a few of examples of women who took the reins in their own lives.

Women of that time and place were in danger of abduction, especially if they were wealthy... but it was preferable to a loveless marriage. The average "knight in shining armor" was a mix of professional assassin and local rapist, so the damsel often arranged to be kidnapped by her preferred suitor or even do the abducting herself:
Marjorie of Carrick (c. 1253-1292) was a countess in her own right, but was married young to an older husband who died in the Crusades in 1271; she was informed of this by her husband's handsome young companion, Robert de Brus. Marjorie, out hunting at the time and far from upset by the news, was so taken by his beauty that she took him back to her castle and held him captive until he agreed to marry her; she must have done something right, because they were married within days. The second of their eleven children was Robert the Bruce himself.

She wants you to bail her out of every situation. You may offer her advice instead, but she'd rather just have your money. She is never satisfied with any situation, and usually nitpicks until the situation is ridiculously out-of-control.

Person A: Dude, ______ is having a really rough time. Maybe we should help her out.